Month: February 2017

On February 8, 2017, the United States Senate confirmed Jefferson Sessions as U.S. Attorney General. This appointment has been widely criticized over Sessions’s civil rights record and hard-line stance on immigration. The Trump administration defends the appointment, citing Sessions’s vote to confirm Attorney General Eric Holder and efforts to award Rosa Parks the Congressional Gold Medal. It has also been reported that Sessions is well-liked by his colleagues in the Senate.

Our findings have been reported by Mother Jones. Here, we describe our methods and results in more detail.

Senators in Twitter space

We have seen previously that useful information can be gleaned from examining co-followership of Twitter accounts. In our previous blog post, we used publicly available data from Twitter to look at network relationships between nodes of interest; these focal nodes included white nationalist groups, media sources, and politicians. Here we turn our attention to Twitter relationships between white nationalist groups and U.S. Senators, again using tools from network science. We included Twitter accounts for 9 white nationalist groups and all U.S. Senators, giving a total of 109 focal nodes. We obtained a list of followers for each focal node using the Twitter API1Twitter data pulled in a two week time span from November 22 to December 6, 2016, giving more than 11.4 million unique followers in total. We used these data to construct a co-follower network between these focal nodes using the methods described previously.

To illustrate that the co-follower network conveys meaningful information, we used community detection. Specifically, we performed modularity maximization using a Louvain algorithm to look for structure in the sub-network consisting of only the 100 Senators (see Figure 1). Community detection yielded three groups: one group consisting entirely of Democrats together with the independent Angus King, and the other two consisting almost entirely of Republicans.2The following are exceptions: Senator Tester is a Democrat placed in the first Republican community, and Senator Donnelly and Senator Heitkamp were placed with the second Republican community. This partisan homogeneity within the detected communities indicates that the co-follower network is indeed capturing important features of the focal nodes and the political interests of their followers.

Figure 1. Communities in the network of senator co-followership.

Senators and white nationalists

To examine the relationship between Senators and the white nationalist community (the set of 9 white nationalist focal nodes), we compute the distance between these two groups on the co-follower network. Specifically, we calculate the geodesic (shortest path) distance from Senators to the white nationalist community (see Figure 2), with distance across a directed edge equal to the reciprocal of the edge weight between nodes.3We computed shortest paths between focal nodes using Dijkstra’s algorithm. To compute the distance to the white nationalist community, we calculated a weighted average (with weights according to PageRank) of the distance to each white nationalist focal node.

Figure 2. Distance between focal nodes in the co-follower network.

Figure 3 shows the resulting distance from each Senator to the white nationalist community, with color indicating a senator’s ideology score (as computed by GovTrack.us).4An analysis of distance in the other direction, from the white nationalist community to Senators, gives similar but less dramatic conclusions.. There is a strong correlation between follower size and distance, with larger numbers of followers associated with greater distances from the white nationalist community.5This reflects the way the co-follower network is constructed, as the edge weights in the co-follower network correspond to the proportion of shared followers. Thus, if node A has a far larger number of followers than node B, the maximum for the edge weight from A to B is the number of followers of B divided by the followers of A (giving a small number). Senator Sessions had nearly 86,000 followers at the time of data retrieval, ranking 22/100 among the Senators. Despite this reasonably large following, the distance from Sessions to the white nationalist community was the closest of all Senators. Indeed, Sessions appears as an outlier in Figure 3. This closeness of Sessions to the white nationalist community reflects an unexpectedly high degree of co-followership. For example, more than 7% of followers of white nationalist nodes also follow Sessions, including 10% of followers of Matthew Heimbach6 Heimbach was featured recently in a New York Timesarticle on the `alt-right’ and 9% of followers of ‘The Right Stuff’. This is the 6th highest proportion of co-followership with the white nationalist community among all Senators, and the five Senators with higher proportions all have far larger followings on Twitter (on the order of 1 million followers or more).7 The six Senators with highest white nationalist co-followership are, in order, Rand Paul, Ted Cruz, Marco Rubio, Bernie Sanders, John McCain, and Jeff Sessions.

Figure 3. Co-followership distance from senators to the white nationalist community. Color indicates each senator’s ideology score, with blue indicating more liberal and red more conservative.

Mouse-over any data point to see the Senator’s name.

What other factors influence the distance from Senators to white nationalists? Party and ideology are obvious candidates, and there appear to be some relationships between these factors and distance. For example, ideology scores closer to 1, indicating more conservative legislative behavior, may correlate with lower white nationalist distances for a given number of followers (i.e. the bottom edge of the dots appears to be redder). A similar pattern can be seen if we color the data by party instead of ideology score. (An interesting exception is Mitch McConnell, who has a very large distance to white nationalist communities given his number of followers. This may indicate a broader range of network ties, perhaps due to his position as Senate Majority Leader). However, in both cases, there is quite a bit of variation in placement, and more analysis would need to be done to confirm these observations.8For example, one could do a regression analysis of ideology score with white nationalist distance, controlling for number of followers.

Geography is another potential factor, but it shows no obvious pattern. Figure 4 shows a map of the average distance from the Senators in each state to the white nationalist community. Any influence of geography, ideology, or party appears secondary to the effect of follower size, where Sessions is a clear outlier.

Figure 4. Co-followership distance from Senators to the white nationalist community by state (averaged over both Senators from each state).

Why is Sessions an outlier? Our data cannot answer that question. Nor can our analysis indicate Sessions’s personal views or the stances that he will take as U.S. Attorney General. But the data do show that white nationalist groups have a strong interest in our new Attorney General.

Twitter data pulled in a two week time span from November 22 to December 6, 2016

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The following are exceptions: Senator Tester is a Democrat placed in the first Republican community, and Senator Donnelly and Senator Heitkamp were placed with the second Republican community.

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We computed shortest paths between focal nodes using Dijkstra’s algorithm. To compute the distance to the white nationalist community, we calculated a weighted average (with weights according to PageRank) of the distance to each white nationalist focal node.

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An analysis of distance in the other direction, from the white nationalist community to Senators, gives similar but less dramatic conclusions.

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This reflects the way the co-follower network is constructed, as the edge weights in the co-follower network correspond to the proportion of shared followers. Thus, if node A has a far larger number of followers than node B, the maximum for the edge weight from A to B is the number of followers of B divided by the followers of A (giving a small number).